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<h1>Path control points and Bezier points</h1>


<p>A <a href="paths.htm">path</a> has a position and orientation component (or channel), and can additionally also have a component that describes a velocity profile. A path is defined by control points that describe the path as a succession of linked segments. Control points are only visible when the path is selected:
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<p align=center><img src="images/pathsCtrl1.jpg"></p>
<p class=imageLabel>[Two simple identical path objects. The path on the right-hand side is selected (control points become visible)]</p>
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<p>The first control point of a path (the start point) is indicated as a sphere, where the remaining of the control points are indicated as cubes. A path can be open or closed. When closed, it becomes cyclic.<br>
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<p align=center><img src="images/pathsCtrl2.jpg"></p>
<p class=imageLabel>[A closed path]</p>
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<p>Each control point has attributes that can describe the path in more details around its vicinity: each control point can describe if and how a Bezier curve should be calculated. Following illustrates this property:<br>
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<p align=center><img src="images/pathsCtrl3.jpg"></p>
<p class=imageLabel>[Two identical path objects. The path on the right-hand side is selected (control points become visible)]</p>
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<p>By default, Bezier points are always visible (also when the object is not selected) and are displayed as small red-green-blue arrows indicating the x-, y- and z-axis of the Bezier point (which effectively is a point with orientation). The Bezier curve section is described by 3 parameters as can be seen in following figure:<br>
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<p align=center><img src="images/pathsCtrl4.jpg"></p>
<p class=imageLabel>[Parameters describing a Bezier curve section]</p>
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<p>The Bezier interpolation factors indicate where the Bezier curve section starts and ends, and the Bezier point count indicates how detailed (or smooth) the curve should be. A Bezier point count of 1 technically disables the Bezier curve interpolation mechanism, but for simplicity, the control point is then referred to as a Bezier point.<br>
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<p>The position and orientation of a control point can be manually adjusted in the <a href="pathEditMode.htm">path edit mode</a>. A Bezier point orientation however cannot be individually adjusted. It is rather automatically calculated. By default, the orientation of the Bezier points will <em>follow</em> the path curvature (if the automatic orientation option is enabled), otherwise they are interpolated with the control points' orientations as illustrated by following figure:<br>
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<p align=center><img src="images/pathsCtrl4.jpg"></p>
<p class=imageLabel>[Two similar path objects, the left one has the automatic orientation enabled]</p>
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<h3 class=recommendedTopics>Recommended topics</h3>
<li><a href="paths.htm">Paths</a></li>
<li><a href="pathPositionCalculationMethod.htm">Path position and length calculation method</a></li>
<li><a href="pathMovementAlongAPath.htm">Movement along a path</a></li>
<li><a href="pathPropertiesDialog.htm">Path properties</a></li>
<li><a href="pathImportExport.htm">Path import/export operations</a></li>
<li><a href="pathEditMode.htm">Path edit mode</a></li>
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